U.S. patent number 4,647,159 [Application Number 06/686,153] was granted by the patent office on 1987-03-03 for gradient index type single lens.
This patent grant is currently assigned to Canon Kabushiki Kaisha. Invention is credited to Takeshi Baba.
United States Patent |
4,647,159 |
Baba |
March 3, 1987 |
Gradient index type single lens
Abstract
In a gradient index type single lens having a gradient index in
a direction perpendicular to the optic axis thereof, the surface of
the single lens on the light beam incidence side when the single
lens is used at a reduced magnification forms a planar surface, the
surface of the single lens on the light beam emergence side forms a
convex surface and are satisfied the following conditions: where
r.sub.2 is the radius of curvature of the surface on said light
beam emergence side, d is the thickness of the single lens, N.sub.0
is the on-axis refractive index of the single lens, and f is the
focal length of the single lens.
Inventors: |
Baba; Takeshi (Yokohama,
JP) |
Assignee: |
Canon Kabushiki Kaisha (Tokyo,
JP)
|
Family
ID: |
24755131 |
Appl.
No.: |
06/686,153 |
Filed: |
December 26, 1984 |
Current U.S.
Class: |
359/654 |
Current CPC
Class: |
G02B
3/0087 (20130101) |
Current International
Class: |
G02B
3/00 (20060101); G02B 003/00 () |
Field of
Search: |
;350/413 |
Foreign Patent Documents
Other References
Nishi et al., "Selfoc Microlens with a Spherical Surface," Applied
Optics, vol. 21, No. 6, Mar. 15, 1982, pp. 1021-1023..
|
Primary Examiner: Corbin; John K.
Assistant Examiner: Gass; Rebecca D.
Attorney, Agent or Firm: Fitzpatrick, Cella, Harper &
Scinto
Claims
I claim:
1. A gradient index type single lens having an gradient index in a
direction perpendicular to the optic axis thereof, wherein the
surface of said single lens on the light beam incidence side when
said single lens is used at a reduced magnification forms a planar
surface and the surface of said single lens on the light beam
emergence side forms a convex surface, said single lens satisfying
the following conditions:
where r.sub.2 is the radius of curvature of the surface on said
light beam emergence side, d is the thickness of said single lens,
N.sub.0 is the on-axis refractive index of said single lens, and f
is the focal length of said single lens.
2. A gradient index type single lens according to claim 1, wherein
said d and said r.sub.2 satisfy the relation that
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a gradient index type single lens
suitable as the collimator lens of a semiconductor laser or the
pickup objective lens or the like of an optical disc.
2. Description of the Prior Art
SELFOC lens (trade name) is well known as a lens having an index
gradient in a direction perpendicular to the optic axis thereof,
i.e., so-called radial gradient index lens, and has been used as an
erect one-to-one magnification imaging element in a copying
apparatus or the like.
In recent years, attempts have been made to use this gradient index
type lens as the pickup objective lens of a digital audio disc or
the like. The use of a plano-convex gradient index type lens is
shown in the 4th topical meeting on gradient-index optical imaging
systems. However, in the single lens shown therein, only the
correction of spherical aberration which is an on-axis aberration
is considered. In contrast, where such lens is actually used as a
pickup objective lens or a collimator lens, not only the on-axis
aberration but also off-axis aberration must be well corrected.
SUMMARY OF THE INVENTION
In view of the above-noted points it is an object of the present
invention to provide an gradient index type single lens in which
spherical aberration and sine condition are well corrected.
The single lens according to the present invention is plano-convex
in shape and, when this single lens is used at a reduced
magnification, the surface thereof on the light beam incidence side
forms a planar surface and the surface thereof on the light beam
emergence side forms a convex surface relative to the image side
(the light beam emergence side), and the above object is achieved
by the single lens satisfying the following conditions:
where r.sub.2 is the radius of curvature of said convex surface, d
is the thickness of the single lens, N.sub.0 is the on-axis
refractive index of the single lens, and f is the focal length of
the single lens. Accordingly, where the single lens according to
the present invention is used as a light pickup objective lens, the
convex surface thereof faces a recording medium, and where and
where the single lens is used as the collimator lens of a
semiconductor laser, the convex surface thereof faces the
semiconductor laser.
Further, the single lens according to the present invention
satisfies the condition that
thereby enabling better correction of aberrations.
In the single lens according to the present invention, installing
the lens in the manner as described above when it is used at a
reduced imaging magnification means that a parallel light beam or a
light beam approximate to a parallel light beam enters or emerges
from the planar surface of the lens.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows the shape of a single lens according to the present
invention.
FIGS. 2A and 2B show the aberrations of an embodiment of the single
lens according to the present invention.
FIG. 3 shows the gradient index of an embodiment of the single lens
according to the present invention.
FIG. 4 is a schematic view showing the single lens according to the
present invention when used as the pickup lens of an optical
disc.
FIGS. 5A and 5B show the aberrations of an embodiment of the single
lens shown in FIG. 4.
FIG. 6 shows an example of the lens support when the single lens
according to the present invention is used as the pickup lens of an
optical disc.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
To correct spherical aberration and sine condition, it is necessary
to make the values of tertiary or third-order spherical aberration
coefficient and coma coefficient small.
In a radial gradient single lens wherein the refractive index N is
expressed as follows relative to the distance r from the optic
axis:
(N.sub.0, N.sub.1, N.sub.2, N.sub.3, N.sub.4 . . . constant),
parameters which contribute to the value of the tertiary aberration
coefficient are N.sub.0, N.sub.1, N.sub.2 and
r.sub.1 : radius of curvature of the first surface
r.sub.2 : radius of curvature of the second surface
d: thickness.
Of these, the on-axis refractive index N.sub.0 can assume only a
value of the order of 1.4-1.8 and therefore, if N.sub.0 is regarded
as N.sub.0 .apprxeq.1.6, parameters which contribute to the
tertiary aberration coefficient are considered to be r.sub.1,
r.sub.2, d, N.sub.1 and N.sub.2.
On the other hand, the required conditions are the following three:
##EQU1## and therefore, even if r.sub.1 is limited to r.sub.1 =
from the fact that one surface is a plane, it is anticipated that
there are many solutions of r.sub.2, d, N.sub.1 and N.sub.2 which
satisfy condition (2). From among these many solutions, ones
capable of correcting high-order aberrations or ones in which the
working distance is appropriate can be selected in accordance with
the conditions of use.
Among r.sub.2, d, N.sub.1 and N.sub.2, those which contribute to
the paraxial amount are r.sub.2, d and N.sub.1 and, as shown in P.
J. Sands: Jour. Opt. Soc. Am., 60, pages 1436-1442 (1970), N.sub.2
is in a linear relation with the tertiary aberration coefficients.
Accordingly, d, N.sub.1, and N.sub.2 which satisfy condition (2)
for a certain r.sub.2 can be found by the following procedures:
(1) d is given arbitrarily;
(2) N.sub.1 is found so that f=constant;
(3) N.sub.2 is found so that I=0; and
(4) The procedures (1)-(3) are repeated with so that d varied
II=0.
After the initial values of the parameters r.sub.2, d, N.sub.1 and
N.sub.2 have been determined by such procedures, each parameter may
be varied as in the case of the conventional lens design to thereby
balance each aberration.
Also, by introducing the high-order coefficients N.sub.3, N.sub.4,
. . . of the gradient index, it is possible to correct spherical
aberration better and achieve a great aperture.
The following facts have become apparent from the above-described
designing process.
First, for the correction of spherical aberration and sine
condition, it is desirable that r.sub.2 and d satisfy the following
conditions:
(1-N.sub.0)f/r.sub.2 indicates the value of the refractive power
borne by the second surface relative to the refractive power of the
entire system, and if this value exceeds the upper limit of
condition (3-1), correction of spherical aberration will become
difficult, and if this value exceeds the lower limit of condition
(3-1), the effect of coma correction by the second surface will not
be obtained.
Also, if d exceeds the lower limit of condition (3-2), the absolute
value of N.sub.1 will increase in order to keep the focal length
constant and thus, manufacture will become difficult and spherical
aberration will be aggravated. If d exceeds the upper limit of
condition (3-2), the working distance will decrease.
For better correction of spherical aberration and sine condition,
it is desirable that the following condition be further
satisfied:
That is, when .vertline.r.sub.2 .vertline. increases and the
refrective power by the second surface decreases, the refractive
power which the gradient index has must be increased in order to
keep the focal length constant, but by increasing d with the
relation of condition (3-3) and suppressing the increase in
gradient index, spherical aberration and sine condition can be
corrected well.
Embodiments of the present invention will hereinafter be described.
Table 1 below shows the lens data of first to sixth embodiments of
the single lens according to the present invention, and as shown in
FIG. 1, r.sub.1 is the radius of curvature of the planar surface,
r.sub.2 is the radius of curvature of the convex surface, and d is
the thickness of the lens. The radius of curvature r.sub.1 of the
planar surface is infinite N.sub.0, N.sub.1, N.sub.2, N.sub.3 and
N.sub.4, as shown in equation (1), are constants which determine
the gradient index of the single lens. Also, the lens data shown
are the values when the focal length is normalized to 1. In the
present invention, the light beam incidence side of the single lens
in a case where a light beam travels from the planar surface toward
the convex surface of the single lens when used at a reduced
magnification as shown in FIG. 1 is defined as the object side, and
the light beam emergence side of the single lens is defined as the
image side and accordingly, the value of the radii of curvature of
the surfaces are positive in a case where the center of curvature
lies more adjacent to the image side than to the surfaces, and are
negative in the converse case.
TABLE 1 ______________________________________ Em- bodi- ment
r.sub.2 d N.sub.0 N.sub.1 N.sub.2 N.sub.3 N.sub.4
______________________________________ 1 -0.5556 1.133 1.6 0.0561
0.9960 0. 0. 2 -0.6479 1.286 1.6 -0.0593 0.5197 1.9460 0. 3 -0.7789
1.577 1.6 -0.0932 0.2555 0.4958 0. 4 -0.9578 1.895 1.6 -0.1767
0.1318 0.0597 0.3408 5 -0.6241 1.307 1.45 -0.1587 0.3440 1.1134 0.
6 -0.8380 1.676 1.75 -0.0574 0.2897 0.5570 0.
______________________________________
Table 2 below shows the values of the back focus S'.sub.k, tertiary
spherical aberration coefficient I, coma coefficient II,
astigmatism coefficient III, Petzval sum P, distortion coefficient
V, .vertline.r.sub.2 /d.vertline. and (1-N.sub.0)/r.sub.2 of the
respective embodiments (No. 1-No. 6) shown in Table 1 when the
object is at infinity.
TABLE 2
__________________________________________________________________________
Embodiment S'.sub.k I II III P V .vertline.r.sub.2 /d.vertline.
(1-N.sub.0)/r.sub.2
__________________________________________________________________________
1 1.05 0.001 0.116 -0.469 0.625 0.875 0.49 1.080 2 0.92 0.267
-0.164 -0.187 0.626 0.619 0.50 0.926 3 0.91 0.063 -0.071 -0.198
0.633 0.586 0.49 0.770 4 0.64 -0.022 -0.053 -0.095 0.667 0.353 0.51
0.626 5 0.84 0.162 -0.163 -0.118 0.709 0.380 0.48 0.721 6 0.91
0.083 -0.045 -0.259 0.574 0.757 0.50 0.895
__________________________________________________________________________
FIGS. 2A and 2B show the aberrations of the third embodiment (No.
3). In FIG. 2A, solid line indicates spherical aberration and
broken line indicates sine condition, and in FIG. 2B, solid line
indicates the curvature of sagittal image plane and broken line
indicates the curvature of tangential image plane. FIG. 3 shows the
gradient index N(r) of the lens shown in the third embodiment in
the direction orthogonal to the optic axis thereof. In FIG. 3, the
ordinate represents the refractive index N and the abscissa
represents the distance from the optic axis (r=0).
The fourth embodiment (No. 4) has a great aperture in which
particularly NA is of the order of 0.5, and is usable as the pickup
objective lens or the like of an optical disc.
As shown in FIGS. 2A and 2B, the various aberrations are well
corrected, and the aberrations of the other lenses are such that NA
is 0.2-0.3 and the half field angle is of the order of 3.degree.,
which means a good performance.
In any of these first to sixth embodiments, as seen from Table 2,
tertiary spherical aberration coefficient and coma coefficient are
well corrected and in making the aperture of the lens great,
high-order spherical aberrations may be corrected by the control of
the coefficient of high-order gradient index.
Also, in the shown embodiments, correction of spherical aberration
is accomplished by the coefficients N.sub.2, N.sub.3, . . . of
gradient index but a similar effect may also be obtained by
introducing a non-spherical surface into the second surface.
This is because for the tertiary spherical aberration coefficient
created by the index gradient, N.sub.2 contributes in the form of
N.sub.2 .times..intg.h.sup.3 (x)dx and for the tertiary coma
coefficient, N.sub.2 contributes in the form of N.sub.2
.times..intg.h.sup.2 (x)h(x)dx, where h(x) is the height of the
paraxial on-axis light ray at a point in a heterogeneous medium and
h(x) is the height of the paraxial principal light ray, and
integration is effected in the direction of the optic axis of the
heterogeneous medium. Accordingly, these integrated values are
determined by only r.sub.1, r.sub.2, d, N.sub.0, N.sub.1, the
object and the position of the entrance pupil, but if the entrance
pupil lies near the lens and the lens is not so long, h(x) will
become a value considerably smaller than h(x) and N.sub.2 will
hardly affect the coma coefficient. That is, the value of the coma
coefficient is determined by only r.sub.1, r.sub.2, d, N.sub.0,
N.sub.1 and the object distance.
It is easy to obtain the correction effect of spherical aberration
by N.sub.2 by the fourth-order non-spherical coefficient of the
second surface, but again in this case, the fourth-order
non-spherical coefficient does not contribute to the coma
coefficient. In the stage in which spherical aberration has been
corrected, the coma coefficient has nothing to do with the position
of the enterance pupil and therefore, if the entrance pupil lies on
the second surface, the contribution of the fourth-order
non-spherical coefficient to the coma coefficient will be 0.
Such a circumstance also basically holds true with respect to
high-order aberration and therefore, the coefficients N.sub.2,
N.sub.3, . . . of the gradient index are nearly equivalent to the
fourth-order, the sixth-order . . . non-spherical coefficients in
the correction of aberrations.
FIG. 4 is a partial schematic view showing a case where the single
lens of the present invention is applied as the pickup objective
lens of an optical disc. In FIG. 4, reference numeral 1 designates
the single lens of the present invention, and reference numeral 2
denotes the glass plate of an optical disc. t represents the
thickness of the glass plate, N.sub.G represents the refractive
index of the glass plate, and WD represents the air space between
the single lens and the glass plate.
A parallel flat plate glass so disposed rearwardly of the optical
system has the function of correcting spherical aberration to the
positive, as is well known, and particularly the tertiary spherical
aberration coefficient is increased by ##EQU2## by the parallel
flat plate glass. (f is the focal length of the entire system.)
Accordingly, during the designing of the aforedescribed single
lens, it is necessary to make the spherical aberration of the
single lens under-corrected by this amount, and it is desirable
that .vertline.r.sub.2 /d.vertline. assume a value somewhat greater
than that in the aforedescribed first to sixth embodiments.
Table 3 below shows two examples (seventh and eighth embodiments)
of the lens data of the single lens 1 when t=1.2 and N.sub.G =1.52
and WD=0.87.
TABLE 3
__________________________________________________________________________
Embodiment r.sub.2 d N.sub.0 N.sub.1 N.sub.2 N.sub.3 N.sub.4
__________________________________________________________________________
7 -2.8811 5.242 1.651 -2.695 .times. 10.sup.-2 1.847 .times.
10.sup.-3 2.900 .times. 10.sup.-5 3.700 .times. 10.sup.-6 8 -3.3240
5.985 1.651 -2.191 .times. 10.sup.-2 1.134 .times. 10.sup.-3 7.113
.times. 10.sup.-5 1.614 .times. 10.sup.-5
__________________________________________________________________________
Table 4 below shows the values of the then focal length f, the air
conversion back focus S'.sub.K of the single lens, the tertiary
aberration coefficients of the entire system and .vertline.r.sub.2
/d.vertline.(1-N.sub.0)f/r.sub.2.
TABLE 4
__________________________________________________________________________
Embodiment f S'.sub.K I II III P V .vertline.r.sub.2 /d.vertline.
(1-N.sub.0)f/r.sub.2
__________________________________________________________________________
7 2.67 1.66 0.039 -0.058 -0.082 0.643 0.373 0.55 0.603 8 3.01 1.59
0.004 -0.050 -0.070 0.647 0.341 0.56 0.590
__________________________________________________________________________
In the present specification, the gradient index has been
represented as shown in equation (1), but it is often the case that
the gradient index is represented by an equation like N(r).sup.2
=N.sub.0 2{1-(gr).sup.2 +h.sub.4 (gr).sup.4 +h.sub.6 (gr).sup.6 + .
. . } and therefore, the values of parameters N.sub.0, g, h.sub.4
and h.sub.6 when the gradient index of the seventh and eighth
embodiments are so represented will be given in Table 5 below.
TABLE 5 ______________________________________ Embodiment N.sub.0 g
h.sub.4 h.sub.6 ______________________________________ 7 1.651
0.1807 2.349 9.044 8 1.651 0.1629 2.200 3.632
______________________________________
FIGS. 5A and 5B show the aberrations of the single lens shown in
the seventh embodiment. The solid line and broken line in FIG. 5A
are the same as those in FIG. 2A, and the solid line and broken
line in FIG. 5B are the same as those in FIG. 2B.
The application of such single lens according to the present
invention can be easily achieved simply by selecting an embodiment
having an appropriate back focus from Table 1 and correcting the
aggravation of spherical aberration by the glass plate 2.
The aberration coefficients in Table 2 and 4 and the aberration
graphs of FIGS. 2 and 5 are all the values in the state in which
the object is at infinity and the entrance pupil is coincident with
the forward principal point position.
Also, in the present invention, it is desirable in the correction
of high-order spherical aberrations that as shown in FIG. 3, the
single lens have a very weak negative or positive index gradient
near the optic axis of the lens. Such a gradient index can be
formed by the optical copolymerizing method which is to be found in
Y. Koike and Y. Ohtsuka: Applied Optics, 22, pages 418-423
(1983).
Also, in the ion exchange method, it is possible by causing ions
having the effect of increasing the refractive index by a short
time of ion exchange, for example, T1.sup.+, Cs.sup.+ or the like,
to be distributed in the marginal portion of the lens.
As described above, in the present invention, one end surface is
planar and yet has a good performance, and this leads not only to
remarkable ease of the working and inspection of the lens but also
to remarkable simplification of the structure of the lens
barrel.
For example, in the case of the pickup objective lens of the
optical disc described in connection with FIG. 4, an auto-focus
mechanism and an auto-tracking mechanism are usually required in
order to cope with the surface vibration and eccentricity of the
optical disc. Therefore, use is made of a method of mounting an
objective lens on an electromagnetically driven movable element
called an actuator and moving the objective lens in the direction
of the optic axis and in a direction orthogonal to the optic
axis.
In such a case, to enhance the responsiveness of the drive, it is
required to reduce the weight of the objective lens itself and of
the lens barrel supporting the lens.
In the present invention, the objective lens is a single lens which
is light in weight, and the first surface of the objective lens is
planar and therefore, the lens barrel and the mechanism for
mounting the lens on the actuator are remarkably simplified.
FIG. 6 shows an example of the manner in which the pickup objective
lens of the optical disc in the present invention is mounted on the
actuator.
Reference numeral 1 designates the single lens in the present
invention, and reference numeral 3 schematically denotes the
movable portion of the actuator. The first surface which is the
planar surface of the single lens 1 may simply be adhesively
connected to the end surface of the movable portion.
Thus, in the single lens of the present invention, the first
surface thereof is a planar surface, whereby the working of the
lens itself is remarkably easy and the structure of the lens barrel
supporting the lens is remarkably simplified and made light in
weight.
Also, even in a case where the lens is used with a prism or the
like being disposed forwardly of the lens, by using the single lens
of the present invention with its end surface being adhesively
secured to the surface of the prism, the structure of the lens
barrel can be simplified and in addition, surface reflection can be
reduced.
In the foregoing, a case where the object point exists at infinity
relative to the planar surface has been shown as an embodiment used
as a reduced magnification, but even if the object point lies at a
finite distance from the planar surface, the performance of the
single lens will be good if it is used at a reduced
magnification.
In the present invention, spherical aberration and sine condition
are corrected by the single lens, but such a single lens is also
effectively usable as element of a combination lens.
As described above, according to the gradient index type single
lens of the present invention, correction of spherical aberration
and sine condition is possible, and such single lens is usable as a
collimator lens or the pickup objective lens of an optical
disc.
* * * * *